Solve for $x$. $7^{8}=7^{8}\cdot7^x$ $x=$
When powers have the same base, $x^m\cdot x^n=x^{m+n}$. Let's expand the powers for ${7^{8}}={7^{8}}\cdot7^x}$. $\begin{aligned} &={\underbrace{7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7}_\text{8 times}}\cdot\underbrace{ }_{x\text{ times}}} \\\\\\ &={\underbrace{7\cdot 7\cdot 7\cdot 7\cdot 7 \cdot 7 \cdot7 \cdot7}_\text{8 times}} \\\\ \end{aligned}$ $x=0$